Question

quadrilateral abcd is the result of rotating quadrilateral abcd by 60° about the origin. select all of the correct statements about the unchanged properties of quadrilateral abcd and quadrilateral abcd. choose all answers that apply. a bc and bc are both parallel to the y - axis. b ∠b and ∠b have the same measure. c d and d have the same coordinates. d none of the above

Explanation:

Step1: Recall properties of rotation

A rotation is a rigid - motion transformation. Rigid - motion transformations preserve side - lengths and angle - measures.

Step2: Analyze option A

When a figure is rotated, the orientation of the sides changes. Just because \(BC\) is parallel to the \(y\) - axis in the pre - image does not mean \(B'C'\) will be parallel to the \(y\) - axis. So, this statement is false.

Step3: Analyze option B

Since rotation is a rigid motion, corresponding angles in the pre - image and the image have the same measure. \(\angle B\) and \(\angle B'\) are corresponding angles, so they have the same measure. This statement is true.

Step4: Analyze option C

A non - zero rotation about the origin will change the coordinates of a point (except for the origin). Point \(D\) and \(D'\) are not the origin, so they do not have the same coordinates. This statement is false.

Step5: Analyze option D

Since option B is true, option D is false.

Answer:

B. \(\angle B\) and \(\angle B'\) have the same measure.